# Effective Drought Communication: Using the Past to Assess the Present and Anticipate the Future

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Data Set and Data Pre-Processing

## 3. Querying for the Most Similar Drought Event

^{5}km

^{2}) does not influence the measure used. This transformation can be accomplished by using the empirical cumulative distribution functions of the characteristics. Further, the similarity between the past drought events and the ongoing drought event can then be expressed by using the ${L}_{1}$ (Manhattan) distance (the sum of absolute differences), i.e., the drought event whose characteristics are situated closest to those of the ongoing drought event is then regarded as the most similar drought event. However, as it might be more helpful to water managers to focus on drought events that were at least as severe as the ongoing drought event, the search space in which the most similar historical drought event is queried for, is restricted towards drought events for which the values in ${\mathbb{I}}^{3}$ are slightly smaller than or effectively larger than these of the ongoing drought event:

## 4. Probabilistic Comparison of the Ongoing Drought Event to Historical Drought Events

- for all ${u}_{1}$,${u}_{2}$ ∈ $\mathbb{I}$,$$\begin{array}{ccc}C({u}_{1},0)=0\hfill & \mathrm{and}\hfill & C(0,{u}_{2})=0\hfill \\ C({u}_{1},1)={u}_{1}\hfill & \mathrm{and}\hfill & C(1,{u}_{2})={u}_{2}\hfill \end{array}$$
- for all ${u}_{1,1}$, ${u}_{1,2}$, ${u}_{2,1}$, ${u}_{2,2}$ ∈ $\mathbb{I}$ for which ${u}_{1,1}$ ≤ ${u}_{1,2}$ and ${u}_{2,1}$ ≤ ${u}_{2,2}$:$$C({u}_{1,2},{u}_{2,2})-C({u}_{1,2},{u}_{2,1})-C({u}_{1,1},{u}_{2,2})+C({u}_{1,1},{u}_{2,1})\ge 0\phantom{\rule{0.166667em}{0ex}}.$$

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Drought events occurring, on 2 November 2012 in Australia displayed in the Lambert Azimuthal Equal Area coordinate system with a resolution of 27.442 km × 29.079 km. The three different drought events are given different colors.

**Figure 2.**Schematic representation of a copula $C({u}_{1},{u}_{2})$ fitted to the marginals ${F}_{1}\left({x}_{1}\right)$ and ${F}_{2}\left({x}_{2}\right)$.

**Figure 3.**The principle of hierarchical nesting of bivariate copulas in the construction of a three-dimensional vine copula through conditional mixtures.

**Figure 4.**Level curves (black) of a bivariate copula, the region (yellow) corresponding to the probability of observing a less (subcritical) event and the region (red) corresponding to the probability of observing a worse (supercritical) event than an event located on the blue level curve.

**Table 1.**Characteristics of drought event at 2 November 2012, experienced at the location indicated in Figure 1 and characteristics of the three most similar drought events in mainland Australia or that include the location.

Affected Area | Duration | Intensity |
---|---|---|

[km^{2}] | [days] | [−] |

ongoing event | ||

$3.83\phantom{\rule{0.166667em}{0ex}}{10}^{5}$ | 59 | $0.999891$ |

three most similar drought events in mainland Australia | ||

$3.53\phantom{\rule{0.166667em}{0ex}}{10}^{5}$ | 88 | $0.999889$ |

$4.06\phantom{\rule{0.166667em}{0ex}}{10}^{5}$ | 49 | $0.999885$ |

$4.50\phantom{\rule{0.166667em}{0ex}}{10}^{5}$ | 114 | $0.999890$ |

three most similar drought events at the location indicated in Figure 1 | ||

$3.53\phantom{\rule{0.166667em}{0ex}}{10}^{5}$ | 88 | $0.999889$ |

$4.06\phantom{\rule{0.166667em}{0ex}}{10}^{5}$ | 49 | $0.999885$ |

$4.04\phantom{\rule{0.166667em}{0ex}}{10}^{5}$ | 109 | $0.999891$ |

**Table 2.**Copula families, structure of the vine copula and values of Kendall’s tau ${\tau}_{K}$. Subscripts 1, 2 and 3 respectively indicate affected area, duration and intensity.

Copula | Family | ${\mathit{\tau}}_{\mathit{K}}$ |
---|---|---|

${C}_{12}$ | t-copula | 0.43 |

${C}_{23}$ | Frank | 0.46 |

${C}_{13|2}$ | Gaussian | 0.12 |

**Table 3.**Values in the cumulative distribution function ${K}_{{C}_{123}}$ of the characteristics of the ongoing drought event as experienced at 2 November 2012 (${K}_{{C}_{123}}\left({w}_{o}\right)$) and of its characteristics upon completion of the event (${K}_{{C}_{123}}\left({w}_{c}\right)$).

${\mathit{K}}_{{\mathit{C}}_{123}}\left({\mathit{w}}_{\mathit{o}}\right)$ | ${\mathit{K}}_{{\mathit{C}}_{123}}\left({\mathit{w}}_{\mathit{c}}\right)$ |
---|---|

0.9776 | 0.9814 |

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**MDPI and ACS Style**

Vernieuwe, H.; De Baets, B.; Verhoest, N.E.C.
Effective Drought Communication: Using the Past to Assess the Present and Anticipate the Future. *Water* **2021**, *13*, 714.
https://doi.org/10.3390/w13050714

**AMA Style**

Vernieuwe H, De Baets B, Verhoest NEC.
Effective Drought Communication: Using the Past to Assess the Present and Anticipate the Future. *Water*. 2021; 13(5):714.
https://doi.org/10.3390/w13050714

**Chicago/Turabian Style**

Vernieuwe, Hilde, Bernard De Baets, and Niko E. C. Verhoest.
2021. "Effective Drought Communication: Using the Past to Assess the Present and Anticipate the Future" *Water* 13, no. 5: 714.
https://doi.org/10.3390/w13050714